Question

What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?f(x) = 5x2 + x + 3A. (-1, 7)B. (0, 3)C. (0, 7) D. (1, 9)

Answer 1

In order to find the solution of the system of equations, we need to find the equation for function g(x). By taking 2 consecutive row of the table, the slope is given by

$m=\frac{5-3}{-1-(-2)}=\frac{2}{1}=2$

and from the given table, we can note that the y-intercept (b) is 7 because at x=0, g(0)=7. Then, the equation of g(x) is

$g(x)=2x+7$

So, the equations will have a common solution when

$f(x)=g(x)$

which implies

$5x^2+x+3=2x+7$

By moving 2x +7 to the left hand side, we obtain

$5x^2-x-4=0$

By applying the quadratic formula,

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

with a=5, b=-1 and c=-4, we get

$x=\frac{1\pm\sqrt{1^2-4(5)(-4)}}{10}$

which gives

$x=\frac{1\pm\sqrt{81}}{10}=\frac{1\pm9}{10}$

Then, one solution is x=1 and a second solution is x=-0.8.

If we insert our first solution into g(x), we get

$g(1)=2(1)+7=9$

So, one solution of our system or equation is (1,9). Therefore, the answer is the last option (1,9)